Beyond NURBS: enhancement of local refinement through T-splines

摘要

The application of NURBS or Non-Uniform B-Splines in free-form optical design has existed for several years. There are cases however where NURBS geometry presents limitations. Tuning the control points of a spline patch may require a large number of faceted polygons to obtain fine structure. The knot pairs in either a uniform or non-uniform B-spline surface require rectangular grid arrangement. Although knot insertion retains surface continuity it adds superfluous complexity as knots require the insertion of entire rows of control points. Adding rows of control points for each new knot to satisfy the NURBS topology needlessly complicates the optical control surface. Stitching together NURBS patches also produces a high probability of continuity error at rib patch junctions which can produce unwanted ripples and holes. The computational cost for altering seed patch control points at NURBS spline patch junctions hampers the performance of a global non-imaging optimizer and reduces the possibility of exploring the more interesting areas of a problem topology within realistic time constraints. Advancements in CAGD or Computer Aided Graphic Design which overcome the common limitations of NURBS can significantly improve free-form possibilities. In most cases control points can be reduced by 60% or more to represent the same free-form geometry. T-splines and other recent CAGD advancements also accelerate local refinement by simplifying control point addition, allowing the designer to increase optical control surface detail where needed.